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Transcript
Chapter 12 The Laws of Thermodynamics Ying Yi PhD 1 PHYS I @ HCCS Outline The first law of thermodynamics The second law of thermodynamics 2 PHYS I @ HCCS First Law of Thermodynamics The First Law of Thermodynamics tells us that the internal energy of a system can be increased by Adding energy to the system Doing work on the system 3 PHYS I @ HCCS Second Law of Thermodynamics Constrains the First Law Establishes which processes actually occur Heat engines are an important application 4 PHYS I @ HCCS Work in Thermodynamic Processes – Assumptions Dealing with a gas Assumed to be in thermodynamic equilibrium Every part of the gas is at the same temperature Every part of the gas is at the same pressure Ideal gas law applies 5 PHYS I @ HCCS Work in a Gas Cylinder The gas is contained in a cylinder with a moveable piston The gas occupies a volume V and exerts pressure P on the walls of the cylinder and on the piston 6 PHYS I @ HCCS Work in a Gas Cylinder, cont. A force is applied to slowly compress the gas The compression is slow enough for all the system to remain essentially in thermal equilibrium W = - P ΔV This is the work done on the gas where P is the pressure throughout the gas 7 PHYS I @ HCCS More about Work on a Gas Cylinder When the gas is compressed ΔV is negative The work done on the gas is positive When the gas is allowed to expand ΔV is positive The work done on the gas is negative When the volume remains constant No work is done on the gas 8 PHYS I @ HCCS Notes about the Work Equation The pressure remains constant during the expansion or compression This is called an isobaric process The previous work equation can be used only for an isobaric process 9 PHYS I @ HCCS PV Diagrams Used when the pressure and volume are known at each step of the process The work done on a gas that takes it from some initial state to some final state is equal in magnitude to the area under the curve on the PV diagram This is true whether or not the pressure stays constant 10 PHYS I @ HCCS PV Diagrams, cont. The curve on the diagram is called the path taken between the initial and final states The work done depends on the particular path Same initial and final states, but different amounts of work are done 11 PHYS I @ HCCS Example 12.1 Work done by an Expanding Gas In a system similar to that shown in active figure 12.1, the gas in the cylinder is at a pressure equal to 1.01 × 105 Pa and the piston has an area of 0.100 𝑚2 . As energy is slowly added to the gas by heat, the piston is pushed up a distance of 4.00 cm. Calculate the work done by the expanding gas on the surroundings, 𝑊𝑒𝑛𝑣 , assuming the pressure remains constant. 12 PHYS I @ HCCS First Law of Thermodynamics Energy conservation law Relates changes in internal energy to energy transfers due to heat and work Applicable to all types of processes Provides a connection between microscopic and macroscopic worlds 13 PHYS I @ HCCS First Law, cont. Energy transfers occur due to By doing work Requires a macroscopic displacement of an object through the application of a force By heat Occurs through the random molecular collisions Both result in a change in the internal energy, DU, of the system 14 PHYS I @ HCCS First Law, Equation If a system undergoes a change from an initial state to a final state, then DU = Uf – Ui = Q + W Q is the energy transferred to the system by heat W is the work done on the system DU is the change in internal energy 15 PHYS I @ HCCS First Law – Signs Signs of the terms in the equation Q Positive if energy is transferred to the system by heat Negative if energy is transferred out of the system by heat W Positive if work is done on the system Negative if work is done by the system DU Positive if the temperature increases Negative if the temperature decreases 16 PHYS I @ HCCS Results of DU Changes in the internal energy result in changes in the measurable macroscopic variables of the system These include Pressure Temperature Volume 17 PHYS I @ HCCS Notes About Work Positive work increases the internal energy of the system Negative work decreases the internal energy of the system This is consistent with the definition of mechanical work 18 PHYS I @ HCCS Example 12.3 Heating a Gas An ideal gas absorbs 5.00 × 103 J of energy while doing 2.00 × 103 J of work on the environment during a constant pressure process. (a) compute the change in the internal energy of the gas. (b) If the internal energy now drops by 4.50 × 103 J and 7.50 × 103 J is expelled from the system, find the change in volume, assuming a constant pressure process at 1.01 × 105 Pa. 19 PHYS I @ HCCS Types of Thermal Processes Isobaric Pressure stays constant Horizontal line on the PV diagram Isovolumetric Volume stays constant Vertical line on the PV diagram Isothermal Temperature stays the same Adiabatic No heat is exchanged with the surroundings 20 PHYS I @ HCCS Adiabatic Expansion, Diagram 21 PHYS I @ HCCS Isothermal Process, Diagram 22 PHYS I @ HCCS General Case Can still use the First Law to get information about the processes Work can be computed from the PV diagram If the temperatures at the endpoints can be found, DU can be found 23 PHYS I @ HCCS Cyclic Processes A cyclic process is one in which the process originates and ends at the same state Uf = Ui and Q = -W The net work done per cycle by the gas is equal to the area enclosed by the path representing the process on a PV diagram 24 PHYS I @ HCCS Heat Engine A heat engine takes in energy by heat and partially converts it to other forms In general, a heat engine carries some working substance through a cyclic process 25 PHYS I @ HCCS Heat Engine, cont. Energy is transferred from a source at a high temperature (Qh) Work is done by the engine (Weng) Energy is expelled to a source at a lower temperature (Qc) 26 PHYS I @ HCCS Thermal Efficiency of a Heat Engine Thermal efficiency is defined as the ratio of the work done by the engine to the energy absorbed at the higher temperature e Weng Qh Qh Qc Qh 1 Qc Qh e = 1 (100% efficiency) only if Qc = 0 No energy expelled to cold reservoir 27 PHYS I @ HCCS Example 12.10 The efficiency of an Engine During one cycle, an engine extracts 2.00 × 103 J of energy from a hot reservoir and transfers 1.50 × 103 J to a cold reservoir. (a) Find the thermal efficiency of the engine. (b) How much work does this engine do in one cycle? (c) What average power does the engine generate if it goes through four cycles in 2.50s? 28 PHYS I @ HCCS Second Law of Thermodynamics No heat engine operating in a cycle can absorb energy from a reservoir and use it entirely for the performance of an equal amount of work Kelvin – Planck statement Means that Qc cannot equal 0 Some Qc must be expelled to the environment Means that e must be less than 100% 29 PHYS I @ HCCS William Thomson, Lord Kelvin 1824 – 1907 British physicist First to propose the use of an absolute temperature scale Formulated a version of the Second Law 30 PHYS I @ HCCS Summary of the First and Second Laws First Law We cannot get a greater amount of energy out of a cyclic process than we put in Second Law We can’t break even 31 PHYS I @ HCCS Second Law, Alternative Statement If two systems are in thermal contact, net thermal energy transfers spontaneously by heat from the hotter system to the colder system The heat transfer occurs without work being done 32 PHYS I @ HCCS Reversible and Irreversible Processes A reversible process is one in which every state along some path is an equilibrium state And one for which the system can be returned to its initial state along the same path An irreversible process does not meet these requirements Most natural processes are irreversible Reversible process are an idealization, but some real processes are good approximations 33 PHYS I @ HCCS Sadi Carnot 1796 – 1832 French Engineer Founder of the science of thermodynamics First to recognize the relationship between work and heat 34 PHYS I @ HCCS Carnot Engine A theoretical engine developed by Sadi Carnot A heat engine operating in an ideal, reversible cycle (now called a Carnot Cycle) between two reservoirs is the most efficient engine possible Carnot’s Theorem: No real engine operating between two energy reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs 35 PHYS I @ HCCS Carnot Cycle 36 PHYS I @ HCCS Carnot Cycle, PV Diagram The work done by the engine is shown by the area enclosed by the curve The net work is equal to Qh - Qc 37 PHYS I @ HCCS Efficiency of a Carnot Engine Carnot showed that the efficiency of the engine depends on the temperatures of the reservoirs TC ec 1 Th Temperatures must be in Kelvins All Carnot engines operating reversibly between the same two temperatures will have the same efficiency 38 PHYS I @ HCCS Notes About Carnot Efficiency Efficiency is 0 if Th = Tc Efficiency is 100% only if Tc = 0 K Such reservoirs are not available The efficiency increases as Tc is lowered and as Th is raised In most practical cases, Tc is near room temperature, 300 K So generally Th is raised to increase efficiency 39 PHYS I @ HCCS Real Engines Compared to Carnot Engines All real engines are less efficient than the Carnot engine Real engines are irreversible because of friction Real engines are irreversible because they complete cycles in short amounts of time 40 PHYS I @ HCCS The First Law and Human Metabolism The First Law can be applied to living organisms The internal energy stored in humans goes into other forms needed by the organs and into work and heat The metabolic rate (ΔU / Δt) is directly proportional to the rate of oxygen consumption by volume 41 PHYS I @ HCCS Measuring Metabolic Rate The metabolic rate is related to oxygen consumption by DVo2 DU 4.8 Dt Dt About 80 W is the basal metabolic rate, just to maintain and run different body organs 42 PHYS I @ HCCS Various Metabolic Rates 43 PHYS I @ HCCS Aerobic Fitness One way to measure a person’s physical fitness is their maximum capacity to use or consume oxygen 44 PHYS I @ HCCS Efficiency of the Human Body Efficiency is the ratio of the mechanical power supplied to the metabolic rate or total power input 45 PHYS I @ HCCS Thank you. 46 PHYS I @ HCCS